Integrable deformations of oscillator chains from quantum algebras

A family of completely integrable nonlinear deformations of systems of N ha rmonic oscillators are constructed from the non-standard quantum deformatio n of the sl(2, R) algebra. Explicit expressions for all the associated inte grals of motion are given and the long-range nature of the interactions int roduced by the deformation is shown to be linked to the underlying co-algeb ra structure. Separability and superintegrability properties of such system s are analysed, and their connection with classical angular momentum chains is used to construct a non-standard integrable deformation of the XXX hype rbolic Gaudin system.